Traditional methods of joint-inversion for log and core data use fractions of different minerals and fluids to represent subsurface rock structures. In most cases, the petrophysical properties of the composite are modeled as averages of the properties for individual components weighted by the corresponding fraction. Most models are linear, some are nonlinear, but all models are analytical approximations to a full solution given by the first principles of physics. There are widely-used methods for joint-inversion analysis that apply to these models and give precise descriptions of the volumetric ratio of mineral and fluid in a rock formation. Such analysis lacks any description relative to the internal rock structure and pore network. Therefore, while the methods have the advantage of being fast due to the availability of efficient matrix inversion methods, they cannot provide critical reservoir parameters such as pore connectivity, tortuosity, elastic properties, capillary pressure, permeabilities, faci, and relative permeability. Furthermore, these analysis methods often use local optimization algorithms, producing different solutions for different initial estimates.
A complete solution using first physical principles in forward models for petrophysical properties, such as NMR properties, electrical properties, elastic properties, nuclear properties, capillary pressure and permeabilities, and others require, in general, additional information about the internal rock structure including the connectivity of the rock pore space or solid frame in addition to the fractional description. There is a need for an inversion method that captures the internal rock structure in addition to the volumetric fractions, and generates a 3D representation of a subsurface rock, which can be used to calculate other petrophysical properties and reservoir parameters, not considered in the original inversion, giving a predictive capability to the method.